NIMCET 2012 Question Paper with solutions

Question : 21 of 120

Marks: +1, -0

If two towers of heights

h_1

and

h_2

subtend angles 60° and 30° respectively at the mid-point of the line joining their feet, then

h_1 : h_2

Solution:

In Δ ABE ,
tan 30° =

h_1/{x/2}

1/√3

⇒ x = 2

√3 h_1

... (i)

and in Δ BCD
tan 60° =

h_2/{x/2}

√3

⇒ x =

{2h_2}/√3

... (ii)
From Eqs. (i) and (ii),

2√3 h_1

{2h_2}/√3

⇒

h_1/h_2

1/3

⇒

h_1:h_2

= 1 : 3

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